Is it true that if a triangle on a unit sphere has 2 sides with equal length then their opposit angles must be equal? I think it is true. I think we can use the spherical sine law. Call the sides with equal lengths $a,b$ and their opposite angles $\alpha,\beta$. Then since $a=b$, $\sin\alpha=\sin\beta$. How do I then say for certain that $\alpha=\beta$? I know that the angles must be $\in (0,\pi)$ (right?). But how can I exclude the possibility of one angle being $\pi-$ the other angle?
Subscribe to:
Post Comments (Atom)
analysis - Injection, making bijection
I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...
-
So if I have a matrix and I put it into RREF and keep track of the row operations, I can then write it as a product of elementary matrices. ...
-
I am asked to prove the density of irrationals in $\mathbb{R}$. I understand how to do this by proving the density of $\mathbb{Q}$ first, na...
-
Can someone just explain to me the basic process of what is going on here? I understand everything until we start adding 1's then after ...
No comments:
Post a Comment